Systems and methods for locating faults on a transmission line with a single tapped load

ABSTRACT

A fault is located in a transmission line with a sending end, a receiving end, and a tapped load connected to the transmission line at a tap node. The tap node divides the transmission line into a sending side and a receiving side. The sending end and the receiving end each include a measuring device. The fault location is determined by obtaining measured circuit parameters including measured pre-fault and faulted current and voltage values at the sending end and at the receiving end of the transmission line. The phase angle difference due to unsynchronized measurement using the measured pre-fault current and the measured pre-fault voltage values may be calculated. The load impedance of the tapped load is calculated. A first fault location is calculated assuming that the fault is located on the sending side of the tap node. A second fault location is calculated assuming that the fault is located on the receiving side of the tap node. The fault location is selected from one of the first fault location and the second fault location, by selecting the fault location having a value within a predetermined range representing a full distance between two nodes.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is related to co-pending and commonly assignedU.S. patent application Ser. No. ______, filed herewith entitled“Systems and Methods for Locating Faults on a Transmission Line withMultiple Tapped Loads” (Attorney Docket No.: ABTT-0231/B000580).

FIELD OF THE INVENTION

[0002] The present invention relates to systems and methods for locatingfaults in a power transmission system, more particularly, a powertransmission system with a single tapped load.

BACKGROUND OF THE INVENTION

[0003] Power transmission lines carry current from generating sources toelectric power users. The power transmission lines are typically highvoltage lines and are typically transformed down to a lower voltage at apower substation, before being distributed to individual electric powerusers (e.g., homes and business buildings). At many power substations,protective relays are included and perform the following functions inconnection with the transmission system: (A) substation control and dataacquisition and (B) protection. Data acquisition typically contains thefunctionality of (a) monitoring the system to ascertain whether it is ina normal or abnormal state; (b) metering, which involves measuringcertain electrical quantities for operational control; and (c) alarming,which provides a warning of some impending problem. Protection typicallyinvolves fast tripping a circuit breaker in response to the detection ofa short-circuit condition (a fault), typically within a few electricalcycles after a fault occurs.

[0004] The detection of a fault in a protection function involvesmeasuring critical system parameters and, when a fault occurs, quicklymaking a rough estimate of the fault location and of certaincharacteristics of the fault so that the faulted line can be isolatedfrom the power grid as quick as possible. A fault occurs when atransmission line, typically due to external causes, diverts electricalcurrent flow from its normal path along the transmission line.

[0005] The major types and causes of faults are insulation faults,caused by design defects, manufacturing defects, improper installation,and aging insulation; electrical faults, caused by lightning surges,switching surges, and dynamic overvoltages; mechanical faults, caused bywind, snow, ice, contamination, trees, and animals; and thermal faults,caused by overcurrent and overvoltage conditions.

[0006] A transmission line typically includes three phase lines,however, a transmission line may also contain one phase, or some othernumber of phases. With a three-phase transmission line, there areseveral types of possible faults. A single-phase fault is a fault from asingle phase to ground (e.g. phase a to ground). A phase-to-phase faultis a fault from one phase to another phase (e.g., phase a to phase b). Aphase-to-phase-to-ground fault is a fault that involves two phases andthe ground (e.g., phase a and phase b to ground). A three-phase fault isa fault that involves all three phases and which may or may not involvethe ground (e.g., phase a, phase b, and phase c to ground).

[0007] In addition to protection functions, digital fault recorders orother processors may be included at a power substation or at a remotesite for calculating fault locations. Fault location does not have to beas fast as protection function, which may be calculated after the faulthas been handled by the protection function, but it should estimate theactual fault location more accurately than a protection function.Accurate fault location facilitates fast location and isolation of adamaged transmission line section, and quick restoration of service toutility customers after repair of the faulted line.

[0008] In addition to supplying power to an electrical user through apower substation with protective relaying, electrical utilities may alsoprovide power to electrical users through a tap, referred to as a tapnode. The tap is a connection point to a phase or phases of the powertransmission system. The tap is connected to a tap lateral, which inturn is connected to and supplies power to a load, referred to as atapped load. There may be more than one tapped load on a tap lateral. Atapped load typically does not have protective relaying, and therefore,does not usually have current and voltage data being measured/recorded.

[0009] Many fault location calculation systems exist for determining thelocation of a fault on a power transmission line. In these systems,voltage and current are measured at one or both ends of a segment of thetransmission line. In some systems, the voltage and current measurementsat both ends of a segment are synchronized. In a synchronized system,the voltage and current readings must have their time clockssynchronized. In some systems, data acquired before the fault conditionis used in the calculation. Some prior fault location calculations areinaccurate for transmission lines with a tapped load, because they weredesigned for use on transmission lines without tapped loads. Some faultlocation calculations are only applicable to certain types of faults,thus a fault type must be selected before or during the calculationprocess, and the performance of these systems may be affected by thefault type selection.

[0010] The prior art does not address calculating fault locations on apower transmission line with a single tapped load, using synchronized orunsynchronized data from two ends (e.g., two protective relays providingcurrent and voltage readings). In a power transmission line with atapped load, the calculations used previously yield less accurateestimations of the fault location. The fault location calculation ontransmission lines with a single tapped load must resolve the mainproblems of a lack of measurement at the tap node, the fact thatmeasurements at both ends of a tapped line may or may not besynchronized, and the fact that a tapped load is normally not a fixedload, but a varying load.

[0011] Therefore, a need exists for a system and method for calculatinga fault location in a transmission line with a single tapped load usingsynchronized or unsynchronized measured data from two ends. The presentinvention satisfies this need.

SUMMARY OF THE PRESENT INVENTION

[0012] The present invention is directed to systems and methods forcalculating a fault location in a transmission line with a tapped loadusing synchronized or unsynchronized measured data from two ends.

[0013] According to an aspect of the invention, a fault is located in atransmission line with a sending end, a receiving end, and a tapped loadconnected to the transmission line at a tap node. The tap node dividesthe transmission line into a sending side and a receiving side. Thesending end and the receiving end each include a measuring device. Thefault location is determined by obtaining measured circuit parametersincluding measured pre-fault and faulted current and voltage values atthe sending end and at the receiving end of the transmission line. Thephase angle difference due to unsynchronized measurement may becalculated using the measured pre-fault current and the measuredpre-fault voltage values. The load impedance of the tapped load iscalculated. A first fault location is calculated assuming that the faultis located on the sending side of the tap node. A second fault locationis calculated assuming that the fault is located on the receiving sideof the tap node. The fault location is selected from one of the firstfault location and the second fault location, by selecting the faultlocation having a value within a predetermined range representing a fulldistance between two nodes.

[0014] According to another aspect of the invention, a fault locationmay be calculated for many types of faults.

[0015] According to a further aspect of the invention, a fault locationmay be calculated for both single phase and three phase transmissionlines.

[0016] According to another aspect of the invention, the measured datamay be synchronized or unsynchronized.

[0017] These and other features of the present invention will be morefully set forth hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention is further described in the detaileddescription that follows, by reference to the noted plurality ofdrawings by way of non-limiting examples of exemplary embodiments of thepresent invention, in which like reference numerals represent similarelements throughout the several views of the drawings, and wherein:

[0019]FIG. 1 is a block diagram of an exemplary transmission line with asingle tapped load;

[0020]FIG. 2 is a block diagram of the exemplary transmission line ofFIG. 1 illustrating exemplary pre-fault conditions;

[0021]FIG. 3a is a block diagram of the exemplary transmission line ofFIG. 1 illustrating exemplary faulted conditions;

[0022]FIG. 3b is a block diagram of the exemplary transmission line ofFIG. 1 illustrating exemplary faulted conditions with positive sequencevalues;

[0023]FIG. 4 is a block diagram of an embodiment of the presentinvention; and

[0024]FIG. 5 is a flow chart showing details of an embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] The present invention is directed to systems and methods forcalculating a fault location in a transmission line with a single tappedload using synchronized or unsynchronized measured data from two ends.

[0026]FIG. 1 illustrates an exemplary transmission line with a singletapped load. As shown in FIG. 1, the transmission line 10 includes asending end S, a receiving end R, and a tap T1, also referred to hereinas tap node T1, between the sending end S and the receiving end R. Aload node L1 is connected to the tap node T1 through a tap lateral. Aload is connected to load node L1. The tap node T1 divides thetransmission line into a sending side 11 and a receiving side 12.

[0027] In order to describe the invention, the following namingconventions will be used. Upper case letters, which are not subscriptedor superscripted, designate a physical value according to Table 1. Thevalues may be measured values, known values, or calculated values. TABLE1 V-Voltage, a complex value I-Current, complex value Z-Impedance,complex value R-Resistance, real value, the real part of impedance ZX-Reactance, real value, the imaginary part of impedance Z

[0028] A lower case letter following a physical value designates whetherthe value is a pre-fault value or a faulted value according to Table 2.The distance to the fault within a transmission line segment isdesignated by m. TABLE 2 p-pre-fault none-faulted (during the fault)m-unit distance to fault within segment, real value

[0029] Typically there are three phases of a fault distinguished infault analysis: pre-fault, faulted and post-fault. Pre-fault is beforethe instant of the fault, faulted is from the instant of the fault tothe actuation of circuit protection, and post-fault is after theactuation of circuit protection.

[0030] A superscript designates the phase or the symmetrical sequencecomponents according to Table 3. TABLE 3 a-Phase a b-Phase b c-Phase c0-Zero sequence 1-Positive sequence 2-Negative sequence

[0031] A subscript designates the node according to Table 4. When twosubscripts are separated by a comma, the subscripts designate the “from”node and the “to” node, respectively. For example the subscript S,T1designates from the sending end S to the tap node T1. When only one nodeis designated, it is designated as the “from” node and the “to” node isground. For example, the subscript T1 designates from tap node T1 toground. Alternately, the “to” node may be designated as 0 for ground.TABLE 4 S-Sending end of transmission line R-Receiving end oftransmission line Tx-Tap node x Lx-Load node x F-Fault point, faultednode, or fault location

[0032] The following examples illustrate the naming convention.V_(T  1)^(a)

[0033] or V_(T  1, 0)^(a)

[0034] represents a complex faulted value of voltage during a fault, ofphase a, from tap node T1 to ground. Ip_(T  4, R)⁰

[0035] represents a zero sequence complex pre-fault value of currentfrom tap node T4 to the receiving end R.

[0036] As shown in FIG. 1, the impedance from the sending end S to thetap node T1 is Z_(ST1). The impedance from the tap node T1 to thereceiving end R is Z_(T1,R). The impedance from the tap node T1 to theload node L1 is Z_(T1,L1) . The impedance of the load is Z_(L1). Theimpedance from the tap node T1 to ground is Z_(T1), which includes theimpedance from Z_(T1,L1) and Z_(L1).

[0037]FIG. 2 illustrates exemplary pre-fault conditions on thetransmission line of FIG. 1. As shown in FIG. 2, Vp¹ _(S) is a positivesequence pre-fault complex voltage from the sending end S to ground. Ip¹_(S,T1) is a positive sequence pre-fault complex current from thesending end S to the tap node T1. Z¹ _(ST1) is a positive sequencecomplex impedance from the sending end S to the tap node Ti. Vp¹ _(T1)is a positive sequence pre-fault complex voltage from the tap node T1 toground. IP¹ _(T1) is a positive sequence pre-fault complex current fromthe tap node T1 to ground. Z¹ _(T1) is a positive sequence compleximpedance from the tap node T1 to ground (including the load impedanceZ_(L1)) Vp¹ _(R) is a positive sequence pre-fault complex voltage fromthe receiving end R to ground. Ip^(I) _(R,T1) is a positive sequencepre-fault complex current from the receiving end R to the tap node T1.Z¹ _(T1,R) is a positive sequence complex impedance from the tap node T1to the receiving end R.

[0038] The values Vp¹ _(S), Ip¹ _(S,T1), Vp^(I) _(R), and Ip₁ _(R,T1)are measured values. The values Z¹ _(S,T1) and Z¹ _(T1,R) are knownvalues, which may be calculated from the distance of the transmissionline segment and the characteristics of the transmission line using wellknown conventional methods.

[0039]FIG. 3a illustrates exemplary faulted conditions on thetransmission line of FIG. 1 with an exemplary fault to ground. As shownin FIG. 3a, a fault node F is located on the transmission line 10. Thefault node F is located between sending end S and tap node T1. As such,the fault provides a path to ground with impedance Z_(F).

[0040] As shown in FIG. 3a, the tap node T1 divides the transmissionline into the sending side 11 and the receiving side 12. The sendingside 11 has an impedance of Z_(S,T1). The receiving side 12 has animpedance of Z_(T1,R).

[0041] The fault node F divides the impedance from sending end S to tapnode T1 into two impedances. The first impedance is (m*Z_(S,T1)) and thesecond impedance is ((1-m)*Z_(S,T1)). In one embodiment, for a distanceof one from the sending end S to the tap node Ti, the fault node F liesa distance of m away from the sending end S, and a distance of (1-m)from the tap node T1. For example, if m is 0.4 and the distance betweensending end S and tap node T1 is ten miles, then the distance from thesending end S to the fault node F is four miles and the distance fromthe fault node F to the tap node T1 is six miles. More generally, thefault node F lies a fraction of m between node h and node i, representedby m_(h,i).

[0042] As shown in FIG. 3b, V¹ _(S) is a positive sequence faultedcomplex voltage from the sending end S to ground. V¹ _(R) is a positivesequence faulted complex voltage from the receiving end R to ground. I₁_(S,T1) is a positive sequence faulted complex current from the sendingend S to the tap node T1. I¹ _(R,T1) is a positive sequence faultedcomplex current from the receiving end R to the tap node T1. Z¹ _(T1) isa positive sequence complex impedance from the tap node T1 to ground(including the tap load impedance Z_(L1)). The values V¹ _(S), I¹_(S,T1), I¹ _(R) and I¹ _(R,T1) are measured values. Z¹ _(F) is anequivalent positive sequence fault impedance from the fault node F toground in the positive sequence network of the line.

[0043] The following assumptions are made: the tapped load is a positivesequence impedance which does not change during the fault; and there isonly one single fault on the transmission line.

[0044] The present invention may use pre-fault measurements to determinethe time difference (or phasor angle difference) of the voltage andcurrent signals from both ends of a power transmission line tosynchronize the measured signals. If the data is already synchronized,the phase angle is zero. Using the pre-fault data, the system alsodetermines the equivalent load impedance of the tapped load. Thesynchronized faulted data and the calculated tapped load impedance areused to perform the initial fault location estimation. One calculationis performed assuming that the fault is on the sending side 11 of thetap node T1. A second calculation is performed assuming that the faultis on the receiving side 12 of the tap node T1. The correct faultlocation is selected from the two calculations. Positive sequencenetwork quantities are used to solve for fault distance.

[0045]FIG. 4 is a block diagram of an exemplary embodiment of a systemin accordance with the present invention. As shown in FIG. 4, the systemincludes a processor 100, a memory 110, a sending end measuring device120, and a receiving end measuring device 130.

[0046] The processor 100 may be any processor suitable for performingcalculations and receiving input data from measuring devices. Forexample, the processor 100 may be a protective relay with oscillographicdata capture or a digital fault recorder. The memory 110 may be used tostore data received from the sending end measuring device 120 and thereceiving end measuring device 130.

[0047] The sending end measuring device 120 measures voltage andcurrent, including both pre-fault and faulted measurements, at thesending end S of the transmission line 10. The sending end measuringdevice 120 may comprise a memory 115 to store pre-fault measurements.The sending end measuring device 120 may comprise a voltage sensor 121and a current sensor 122. The voltage sensor 121 and current sensor 122may output an analog signal. The sending end measuring device 120 mayconvert the analog signal to a digital signal using known analog todigital techniques before transmission over data link 135. The sendingend measuring device 120 may further convert the digital signal intovectors representing current and voltage, Vp¹ _(S), Ip¹ _(S,T1), V¹_(S), and I¹ _(S,T1) at the sending end S.

[0048] The receiving end measuring device 130 measures voltage andcurrent, including both pre-fault and faulted measurements, at thereceiving end R of the transmission line 10. The receiving end measuringdevice 130 may comprise a memory 115 to store pre-fault measurements.The receiving end measuring device 130 may comprise a voltage sensor 121and a current sensor 122. The voltage sensor and current sensor mayoutput an analog signal. The receiving end measuring device 130 mayconvert the analog signal to a digital signal using known analog todigital techniques before transmission over data link 135. The receivingend measuring device 130 may further convert the digital signal intovectors representing current and voltage, Vp¹ _(R), Ip¹ _(R,T1), V¹_(R), and I¹ _(R,T1) at the receiving end R.

[0049] The measuring devices 120, 130 are connected to the processor 100via a data link 135. The data link 135 may be a modem, a local areanetwork, or any suitable data link.

[0050]FIG. 5 is a flow chart showing further details of the operation ofthe system of FIG. 4 and of an embodiment of a method in accordance withthe present invention. As shown in FIG. 5, at step 200, the measuredvalues are obtained. The pre-fault measured values are Vp¹ _(S), Ip¹_(S,T1), Vp¹ _(R), and Ip¹ _(R,T1). The faulted measured values are V¹_(S), I¹ _(S,I1), V¹ _(R), and I¹ _(R,T1).

[0051] At step 210, the phase angle difference, 6, is calculated as avector e^(lδ) if the data is unsynchronized, using pre-fault dataaccording to the following equation. If the data is synchronized thephase angle difference is zero. $\begin{matrix}{e^{j\quad \delta} = \frac{{Vp}_{S}^{1} - {Z_{S,{T\quad 1}}^{1}{Ip}_{S,{T\quad 1}}^{1}}}{{Vp}_{R}^{1} - {Z_{R,{T\quad 1}}^{1}{Ip}_{R,{T\quad 1}}^{1}}}} & {{Equation}\quad 1}\end{matrix}$

[0052] At step 220, the load impedance of tap node T1 is calculatedusing pre-fault data and the phase angle difference according to thefollowing equation. $\begin{matrix}{Z_{T\quad 1}^{1} = {\frac{{Vp}_{T\quad 1}^{1}}{{Ip}_{S,{T\quad 1}}^{1} + {e^{j\quad \delta}{Ip}_{R,{T\quad 1}}^{1}}} = \frac{{Vp}_{S}^{1} - {Z_{S,{T\quad 1}}^{1}{Ip}_{S,{T\quad 1}}^{1}}}{{Ip}_{S,{T\quad 1}}^{1} + {e^{j\quad \delta}{Ip}_{R,{T\quad 1}}^{1}}}}} & {{Equation}\quad 2}\end{matrix}$

[0053] At step 230, a first fault location, M_(S,T1) is calculatedassuming that the fault node F is located on the sending side 11. Thefirst fault location is calculated from Equation 3. A universal networkis used for fault location calculations of all fault types in thethree-phase transmission line. The fault impedance, and thezero/negative sequence network that exists for the type of a fault, isrepresented in the positive sequence network of the tapped line by anequivalent balanced three-phase fault impedance network connected at thefault location to form the universal network. In this manner, a faultlocation may be calculated for any type of fault. $\begin{matrix}{m_{S,{T\quad 1}} = \frac{\begin{matrix}{V_{S}^{1} - {e^{j\quad \delta}V_{R}^{1}} + {Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}} +} \\{Z_{S\quad T\quad 1}^{1}\left( {{e^{j\quad \delta}I_{S\quad T\quad 1}^{1}} - \frac{{e^{j\quad \delta}V_{R}^{1}} - {Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}}}{Z_{T\quad 1}^{1}}} \right)}\end{matrix}}{\begin{matrix}{{Z_{S,{T\quad 1}}^{1}I_{S,{T\quad 1}}^{1}} +} \\{Z_{S,{T\quad 1}}^{1}\left( {{e^{j\quad \delta}I_{R,{T\quad 1}}^{1}} - \frac{{e^{j\quad \delta}V_{R}^{1}} - {Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}}}{Z_{T\quad 1}^{1}}} \right)}\end{matrix}}} & {{Equation}\quad 3}\end{matrix}$

[0054] At step 240, a second fault location, mR,T is calculated assumingthat the fault node F is located on the receiving side 12. The secondfault location is calculated from Equation 4. $\begin{matrix}{m_{R,{T\quad 1}} = \frac{\begin{matrix}{{e^{j\quad \delta}V_{R}^{1}} - V_{S}^{1} + {Z_{S,{T\quad 1}}^{1}I_{S,{T\quad 1}}^{1}} +} \\{Z_{R,{T\quad 1}}^{1}\left( {I_{S\quad t\quad 1}^{1} - \frac{V_{S}^{1} - {Z_{S,{T\quad 1}}^{1}I_{S,{T\quad 1}}^{1}}}{Z_{T\quad 1}^{1}}} \right)}\end{matrix}}{\begin{matrix}{{Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}} +} \\{Z_{R,{T\quad 1}}^{1}\left( {I_{S,{T\quad 1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T\quad 1}}^{1}I_{S,{T\quad 1}}^{1}}}{Z_{T\quad 1}^{1}}} \right)}\end{matrix}}} & {{Equation}\quad 4}\end{matrix}$

[0055] At step 250 the correct solution is selected. When a correctassumption is made, the resulting fault location estimation is alwayswithin some predetermined range, if not, the result will be outside ofthe predetermined range. This criterion is used to select the accuratefault location result from the two estimations. The predetermined rangeis a range selected to represent the full distance between two nodes. Inthe present embodiment, the predetermined range for sending side is fromzero to 1.0, which represent the distance between the sending node S andthe tap node T1 when assuming that the fault lies between the sendingnode S and the tap node T1. Similarly, the predetermined range forreceiving side is also from zero to 1.0, which represent the distancebetween the receiving node R and the tap node T1 when assuming that thefault lies between the receiving node R and the tap node T1. A resultoutside of the predetermined range cannot be correct, as it lies at apoint outside of the distance between the two nodes. For example, usinga unitary predetermined value of m, where the range of 0.0 to 1.0represents the distance between two nodes, if m_(S,T1) is calculated tobe 2.4 in step 230 and M_(R,T1) is calculated to be 0.4 in step 240,then m_(R,T1) is selected, m 0.4 , and the fault node F is on thereceiving side 12. Selecting 2.4 would be contrary to the assumptionthat the fault is located on the sending side 11.

[0056] In another embodiment, the transmission line is a single-phasetransmission line, the equations are the same except that the referencesto the positive sequence component is replaced by the phase quantities,and the equivalent fault impedance is the actual fault impedance.

[0057] As can be appreciated, the above described system and method meetthe aforementioned need for systems and methods for calculating a faultlocation in a transmission line with a single tapped load usingsynchronized or unsynchronized measured data from two ends.

[0058] Although not required, the present invention may be embodied inthe form of program code (i.e., instructions) stored on acomputer-readable medium, such as a magnetic, electrical, or opticalstorage medium, including without limitation a floppy diskette, CD-ROM,CD-RW, DVD-ROM, DVD-RAM, magnetic tape, flash memory, hard disk drive,or any other machine-readable storage medium, wherein, when the programcode is loaded into and executed by a machine, such as a computer, themachine becomes an apparatus for practicing the invention. The presentinvention may also be embodied in the form of program code that istransmitted over some transmission medium, such as over electricalwiring or cabling, through fiber optics, over a network, including theInternet or an intranet, or via any other form of transmission, wherein,when the program code is received and loaded into and executed by amachine, such as a computer, the machine becomes an apparatus forpracticing the invention. When implemented on a general-purposeprocessor, the program code combines with the processor to provide aunique apparatus that operates analogously to specific logic circuits.

[0059] It is to be understood that the foregoing examples have beenprovided merely for the purpose of explanation and are in no way to beconstrued as limiting of the present invention. Where the invention hasbeen described with reference to embodiments, it is understood that thewords which have been used herein are words of description andillustration, rather than words of limitation. Further, although theinvention has been described herein with reference to particularstructure, materials and/or embodiments, the invention is not intendedto be limited to the particulars disclosed herein. Rather, the inventionextends to all functionally equivalent structures, methods and uses,such as are within the scope of the appended claims. Those skilled inthe art, having the benefit of the teachings of this specification, mayeffect numerous modifications thereto and changes may be made withoutdeparting from the scope and spirit of the invention in its aspects.

What is claimed is:
 1. A method for locating a fault in a transmissionline, the transmission line comprising a sending end and a receivingend, a tapped load connected to the transmission line at a tap node, thetap node dividing the transmission line into a sending side and areceiving side, the sending end comprising a measuring device, thereceiving end comprising a measuring device, the method comprising:obtaining measured circuit parameters including measured current andvoltage values at the sending end and at the receiving end of thetransmission line; calculating a load impedance of the tapped load;calculating a first fault location assuming that the fault is located onthe sending side of the tap node; calculating a second fault locationassuming that the fault is located on the receiving side of the tapnode; and selecting the calculated fault location from one of either thefirst fault location and the second fault location, by selecting thefault location having a value within a predetermined range.
 2. Themethod of claim 1 further comprising calculating a phase angledifference due to unsynchronized measurement using the measuredpre-fault current and the measured pre-fault voltage values.
 3. Themethod of claim 2 wherein the obtaining measured circuit parametersfurther comprises obtaining measured circuit parameters from the sendingend measuring device and the receiving end measuring device.
 4. Themethod of claim 2 wherein the obtaining measured circuit parametersfurther comprises obtaining the values, Vp¹ _(S) Ip¹ _(S,T1), Vp¹ _(R),Ip¹ _(R,T1), V¹ _(S), I¹ _(S,T1), V¹ _(R), and I¹ _(R,T1) where: Vp¹_(S) is the positive sequence pre-fault complex voltage from the sendingend to ground, Ip¹ _(S,T1) is the positive sequence pre-fault complexcurrent from the sending end to the tap node, Vp¹ _(R) is the positivesequence pre-fault complex voltage from the receiving end to ground, IP¹_(R,T1) is the positive sequence pre-fault complex current from thereceiving end to the tap node, V¹ _(S) is the positive sequence faultedcomplex voltage from the sending end to ground, I¹ _(S,T1) is thepositive sequence faulted complex current from the sending end to thetap node, V¹ _(R) is the positive sequence faulted complex voltage fromthe receiving end to ground, and I¹ _(R,T1) is the positive sequencefaulted complex current from the receiving end to the tap node, and thetransmission line is a three phase transmission line.
 5. The method ofclaim 4 wherein the calculating a phase angle further comprisescalculating the phase angle, 8, according to the following equation:$e^{j\quad \delta} = \frac{{Vp}_{S}^{1} - {Z_{S,{T\quad 1}}^{1}{Ip}_{S,{T\quad 1}}^{1}}}{{Vp}_{R}^{1} - {Z_{R,{T\quad 1}}^{1}{Ip}_{R,{T\quad 1}}^{1}}}$

where: Z¹ _(S,T1) is the positive sequence complex impedance from thesending end to the tap node, and Z¹ _(R,T1) is the positive sequencecomplex impedance from the receiving end to the tap node.
 6. The methodof claim 4 wherein the measured data is synchronized and the phaseangle, δ, is zero.
 7. The method of claim 5 wherein the calculating aload impedance of the tapped load comprises calculating the loadimpedance of the tapped load according to the following equation:$Z_{T\quad 1}^{1} = \frac{{Vp}_{S}^{1} - {Z_{S,{T\quad 1}}^{1}{Ip}_{S,{T\quad 1}}^{1}}}{{Ip}_{S,{T\quad 1}}^{1} + {e^{j\quad \delta}{Ip}_{R,{T\quad 1}}^{1}}}$

where Z¹ _(T1) is the positive sequence complex impedance of the tapnode.
 8. The method of claim 7 wherein the calculating a first faultlocation comprises calculating a first fault location according to thefollowing equation: $m_{S,{T\quad 1}} = \frac{\begin{matrix}{V_{S}^{1} - {e^{j\quad \delta}V_{R}^{1}} + {Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}} +} \\{Z_{S,{T\quad 1}}^{1}\left( {{e^{j\quad \delta}I_{R,{T\quad 1}}^{1}} - \frac{{e^{j\quad \delta}V_{R}^{1}} - {Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}}}{Z_{T\quad 1}^{1}}} \right)}\end{matrix}}{\begin{matrix}{{Z_{S,{T\quad 1}}^{1}I_{S,{T\quad 1}}^{1}} +} \\{Z_{S,{T\quad 1}}^{1}\left( {{e^{j\quad \delta}I_{R,{T\quad 1}}^{1}} - \frac{{e^{j\quad \delta}V_{R}^{1}} - {Z_{R,{T\quad 1}}^{1}e^{j\quad \delta}I_{R,{T\quad 1}}^{1}}}{Z_{T\quad 1}^{1}}} \right)}\end{matrix}}$

where M_(S,T1) is the calculated first fault location.
 9. The method ofclaim 8 wherein the calculating a second fault location comprisescalculating a second fault location according to the following equation:$m_{R,{T1}} = \frac{{^{j\delta}V_{R}^{1}} - V_{S}^{1} + {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}} + {Z_{R,{T1}}^{1}\left( {I_{S,{T1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}{{Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}} + {Z_{R,{T1}}^{1}\left( {I_{S,{T1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}$

where M_(R,T1) is the calculated second fault location.
 10. The methodof claim 9 wherein the selecting the calculated fault location comprisesselecting the calculated fault location from one of either m_(S,T1) andm_(R,T1) by selecting the one having a value within a predeterminedrange representing a full distance between two nodes.
 11. The method ofclaim 10 wherein the predetermined range is from zero to one.
 12. Asystem for locating a fault in a transmission line having a sending endand a receiving end and a tapped load connected to the transmission lineat a tap node, the tap node dividing the transmission line into asending side and a receiving side, the system comprising: a processorfor calculating a fault location in the transmission line; a sending endmeasuring device connected to the processor for taking pre-fault andfaulted measurements of the sending end of the transmission line; areceiving end measuring device connected to the processor for takingpre-fault and faulted measurements of the receiving end of thetransmission line; and wherein the processor is adapted to obtainmeasured circuit parameters including measured current and voltagevalues from the sending end measuring device and the receiving endmeasuring device, calculate a load impedance of the tapped load,calculate a first fault location assuming that the fault is located onthe sending side of the tap node, calculate a second fault locationassuming that the fault is located on the receiving side of the tapnode; and select the calculated fault location from one of the firstfault location and the second fault location, by selecting the faultlocation having a value within a predetermined range.
 13. The system ofclaim 12 wherein the processor is further adapted to calculate a phaseangle difference due to unsynchronized measurement using the measuredpre-fault current and the measured pre-fault voltage values.
 14. Thesystem of claim 13 wherein the sending end measuring device comprises avoltage sensor.
 15. The system of claim 13 wherein the sending endmeasuring device comprises a current sensor.
 16. The system of claim 13wherein the receiving end measuring device comprises a voltage sensor.17. The system of claim 13 wherein the receiving end measuring devicecomprises a current sensor.
 18. The system of claim 13 wherein thesending end measuring device is connected to the processor through adata link.
 19. The system of claim 13 wherein the receiving endmeasuring device is connected to the processor through a data link. 20.The system of claim 13 wherein the sending end measuring devicecomprises a memory for storing pre-fault measurements.
 21. The system ofclaim 13 wherein the receiving end measuring device comprises a memoryfor storing pre-fault measurements.
 22. The system of claim 13 whereinthe processor is adapted to obtain the values, Vp¹ _(S), IP¹ _(S,T1),Vp¹ _(R) Ip¹ _(R,T1), V¹ _(S), I¹ _(S,T1), V¹ _(R), and I¹ _(R,T1)where: Vp¹ _(S) is the positive sequence pre-fault complex voltage fromthe sending end to ground, Ip_(S,T1) is the positive sequence pre-faultcomplex current from the sending end to the tap node, Vp¹ _(R) is thepositive sequence pre-fault complex voltage from the receiving end toground, Ip¹ _(R,T1) is the positive sequence pre-fault complex currentfrom the receiving end to the tap node, V¹ _(S) is the positive sequencefaulted complex voltage from the sending end to ground, I¹ _(S,T1) isthe positive sequence faulted complex current from the sending end tothe tap node, V¹ _(R) is the positive sequence faulted complex voltagefrom the receiving end to ground, and I¹ _(R,T1) is the positivesequence faulted complex current from the receiving end to the tap node,and the transmission line is a three phase transmission line.
 23. Thesystem of claim 22 wherein the processor is adapted to calculate thephase angle, 6, according to the following equation:$^{j\delta} = \frac{{Vp}_{S}^{1} - {Z_{S,{T1}}^{1}{Ip}_{S,{T1}}^{1}}}{{Vp}_{R}^{1} - {Z_{R,{T1}}^{1}{Ip}_{R,{T1}}^{1}}}$

where: Z¹ _(S,T1) is the positive sequence complex impedance from thesending end to the tap node, and Z¹ _(R,T1) is the positive sequencecomplex impedance from the receiving end to the tap node.
 24. The systemof claim 22 wherein the measured data is synchronized and the phaseangle, δ, is zero.
 25. The system of claim 23 wherein the processor isadapted to calculate a first fault location according to the followingequation: $m_{S,{T1}} = {\quad\frac{\begin{matrix}{V_{S}^{1} - {^{j\delta}V_{R}^{1}} + {Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}} +} \\{Z_{S,{T1}}^{1}\left( {{^{j\delta}I_{R,{T1}}^{1}} - \frac{{^{j\delta}V_{R}^{1}} - {Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}\end{matrix}}{{Z_{S,{T1}}^{1}I_{S,{T1}}^{1}} + {Z_{S,{T1}}^{1}\left( {{^{j\delta}I_{R,{T1}}^{1}} - \frac{{^{j\delta}V_{R}^{1}} - {Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}}$

where m_(S,T1) is the calculated first fault location.
 26. The system ofclaim 25 wherein the processor is adapted to calculate a second faultlocation according to the following equation:$m_{R,{T1}} = \frac{{^{j\delta}V_{R}^{1}} - V_{S}^{1} + {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}} + {Z_{R,{T1}}^{1}\left( {I_{S,{T1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}{{Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}} + {Z_{R,{T1}}^{1}\left( {I_{S,{T1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}$

where m_(R,T1) is the calculated second fault location.
 27. The systemof claim 26 wherein the processor is adapted to select the calculatedfault location from one of either m_(S,T1) and m_(R,T1) by selecting theone having a value within a predetermined range representing a fulldistance between two nodes.
 28. The system of claim 27 wherein thepredetermined range is from zero to one.
 29. The system of claim 12wherein the transmission line is a single phase transmission line.
 30. Acomputer-readable medium having instructions stored thereon for locatinga fault in a transmission line, the transmission line comprising asending end and a receiving end, a tapped load connected to thetransmission line at a tap node, the tap node dividing the transmissionline into a sending side and a receiving side, the sending endcomprising a measuring device, the receiving end comprising a measuringdevice, the instructions, when executed on a processor, causing theprocessor to perform the following: obtaining measured circuitparameters including measured current and voltage values at the sendingend and at the receiving end of the transmission line; calculating aload impedance of the tapped load; calculating a first fault locationassuming that the fault is located on the sending side of the tap node;calculating a second fault location assuming that the fault is locatedon the receiving side of the tap node; and selecting the calculatedfault location from one of either the first fault location and thesecond fault location, by selecting the fault location having a valuewithin a predetermined range.
 31. The computer readable medium of claim30 further comprising calculating a phase angle difference due tounsynchronized measurement using the measured pre-fault current and themeasured pre-fault voltage values;
 32. The computer-readable medium ofclaim 30 wherein the obtaining measured circuit parameters furthercomprises obtaining measured circuit parameters from the sending endmeasuring device and the receiving end measuring device.
 33. Thecomputer-readable medium of claim 31 wherein the obtaining measuredcircuit parameters further comprises obtaining the values, Vp¹ _(S), Ip¹_(S,T1), Vp¹ _(R), Ip¹ _(R,T1), V¹ _(S), I¹ _(S,T1), V¹ _(R), and I¹_(R,T1) where: Vp¹ _(S) is the positive sequence pre-fault complexvoltage from the sending end to ground, Ip¹ _(S,T1) is the positivesequence pre-fault complex current from the sending end to the tap node,Vp¹ _(R) is the positive sequence pre-fault complex voltage from thereceiving end to ground, IP¹ _(R,T1) is the positive sequence pre-faultcomplex current from the receiving end to the tap node, V¹ _(S) is thepositive sequence faulted complex voltage from the sending end toground, I¹ _(S,T1) is the positive sequence faulted complex current fromthe sending end to the tap node, V¹ _(R) is the positive sequencefaulted complex voltage from the receiving end to ground, and I¹ _(R,T1)is the positive sequence faulted complex current from the receiving endto the tap node, and the transmission line is a three phase transmissionline.
 34. The computer-readable medium of claim 33 wherein thecalculating a phase angle further comprises calculating the phase angle,δ, according to the following equation:$^{j\delta} = \frac{{Vp}_{S}^{1} - {Z_{S,{T1}}^{1}{Ip}_{S,{T1}}^{1}}}{{Vp}_{R}^{1} - {Z_{R,{T1}}^{1}{Ip}_{R,{T1}}^{1}}}$

where: Z_(S,T1) is the positive sequence complex impedance from thesending end to the tap node, and Z¹ _(R,T1) is the positive sequencecomplex impedance from the receiving end to the tap node.
 35. Thecomputer-readable medium of claim 33 wherein the measured data issynchronized and the phase angle, δ, is zero.
 36. The computer-readablemedium of claim 34 wherein the calculating a load impedance of thetapped load comprises calculating the load impedance of the tapped loadaccording to the following equation:$Z_{T1}^{1} = \frac{{Vp}_{S}^{1} - {Z_{S,{T1}}^{1}{Ip}_{S,{T1}}^{1}}}{{Ip}_{S,{T1}}^{1} + {^{j\delta}{Ip}_{R,{T1}}^{1}}}$

where Z¹ _(T1) is the positive sequence complex impedance of the tapnode.
 37. The computer-readable medium of claim 36 wherein thecalculating a first fault location comprises calculating a first faultlocation according to the following equation:$m_{S,{T1}} = {\quad\frac{\begin{matrix}{V_{S}^{1} - {^{j\delta}V_{R}^{1}} + {Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}} +} \\{Z_{S,{T1}}^{1}\left( {{^{j\delta}I_{R,{T1}}^{1}} - \frac{{^{j\delta}V_{R}^{1}} - {Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}\end{matrix}}{{Z_{S,{T1}}^{1}I_{S,{T1}}^{1}} + {Z_{S,{T1}}^{1}\left( {{^{j\delta}I_{R,{T1}}^{1}} - \frac{{^{j\delta}V_{R}^{1}} - {Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}}$

where m_(S,T1) is the calculated first fault location.
 38. Thecomputer-readable medium of claim 37 wherein the calculating a secondfault location comprises calculating a second fault location accordingto the following equation:$m_{R,{T1}} = \frac{{^{j\delta}V_{R}^{1}} - V_{S}^{1} + {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}} + {Z_{R,{T1}}^{1}\left( {I_{S,{T1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}{{Z_{R,{T1}}^{1}^{j\delta}I_{R,{T1}}^{1}} + {Z_{R,{T1}}^{1}\left( {I_{S,{T1}}^{1} - \frac{V_{S}^{1} - {Z_{S,{T1}}^{1}I_{S,{T1}}^{1}}}{Z_{T1}^{1}}} \right)}}$

where m_(R,T1) is the calculated second fault location.
 39. Thecomputer-readable medium of claim 38 wherein the selecting thecalculated fault location comprises selecting the calculated faultlocation from one of either m_(S,T1) and m_(R,T1) by selecting the onehaving a value within a predetermined range representing a full distancebetween two nodes.
 40. The computer-readable medium of claim 39 whereinthe predetermined range is from zero to one.
 41. The computer-readablemedium of claim 30 wherein the transmission line is a single phasetransmission line.